Showing papers on "Random effects model published in 1994"

Analysis of longitudinal data

Abstract: 1. Introduction 2. Design considerations 3. Exploring longitudinal data 4. General linear models 5. Parametric models for covariance structure 6. Analysis of variance methods 7. Generalized linear models for longitudinal data 8. Marginal models 9. Random effects models 10. Transition models 11. Likelihood-based methods for categorical data 12. Time-dependent covariates 13. Missing values in longitudinal data 14. Additional topics Appendix Bibliography Index

A random-effects ordinal regression model for multilevel analysis.

Abstract: A random-effects ordinal regression model is proposed for analysis of clustered or longitudinal ordinal response data. This model is developed for both the probit and logistic response functions. The threshold concept is used, in which it is assumed that the observed ordered category is determined by the value of a latent unobservable continuous response that follows a linear regression model incorporating random effects. A maximum marginal likelihood (MML) solution is described using Gauss-Hermite quadrature to numerically integrate over the distribution of random effects. An analysis of a dataset where students are clustered or nested within classrooms is used to illustrate features of random-effects analysis of clustered ordinal data, while an analysis of a longitudinal dataset where psychiatric patients are repeatedly rated as to their severity is used to illustrate features of the random-effects approach for longitudinal ordinal data.

A computationally practical simulation estimator for panel data

Abstract: In this paper I develop a practical extension of McFadden's method of simulated moments estimator for limited dependent variable models to the panel data case. The method is based on a factorization of the MSM first order condition into transition probabilities, along with the development of a new highly accurate method for similating these transition probabilities. A series of Monte-Carlo tests show that this MSM estimator performs quite well relative to quadrature-based ML estimators, even when large numbers of quadrature points are employed. The estimator also performs well relative to simulated ML, even when a highly accurate method is used to simulate the choice probabilities. In terms of computational speed, complex panel data models involving random effects and ARMA errors may be estimated via MSM in times similar to those necessary for estimation of simple random effects models via ML-quadrature.

Modelling progression of CD4-lymphocyte count and its relationship to survival time.

Abstract: The purpose of this article is to model the progression of CD4-lymphocyte count and the relationship between different features of this progression and survival time. The complicating factors in this analysis are that the CD4-lymphocyte count is observed only at certain fixed times and with a high degree of measurement error, and that the length of the vector of observations is determined, in part, by the length of survival. If probability of death depends on the true, unobserved CD4-lymphocyte count, then the survival process must be modelled. Wu and Carroll (1988, Biometrics 44, 175-188) proposed a random effects model for two-sample longitudinal data in the presence of informative censoring, in which the individual effects included only slopes and intercepts. We propose methods for fitting a broad class of models of this type, in which both the repeated CD4-lymphocyte counts and the survival time are modelled using random effects. These methods permit us to estimate parameters describing the progression of CD4-lymphocyte count as well as the effect of differences in the CD4 trajectory on survival. We apply these methods to results of AIDS clinical trials.

Random-effects regression models for clustered data with an example from smoking prevention research.

Abstract: A random-effects regression model is proposed for analysis of clustered data. Unlike ordinary regression analysis of clustered data, random-effects regression models do not assume that each observation is independent but do assume that data within clusters are dependent to some degree. The degree of this dependency is estimated along with estimates of the usual model parameters, thus adjusting these effects for the dependency resulting from the clustering of the data. A maximum marginal likelihood solution is described, and available statistical software for the model is discussed. An analysis of a dataset in which students are clustered within classrooms and schools is used to illustrate features of random-effects regression analysis, relative to both individual-level analysis that ignores the clustering of the data, and classroom-level analysis that aggregates the individual data.

Use and Misuse of Mixed Model Analysis of Variance in Ecological Studies

Abstract: Analysis of variance is one of the most commonly used statistical techniques among ecologists and evolutionary biologists. Because many ecological experiments involve random as well as fixed effects, the most appropriate analysis of variance model to use is often the mixed model. Consideration of effects in an analysis of variance as fixed or random is critical if correct tests are to be made and if correct inferences are to be drawn from these tests. A literature review was conducted to determine whether authors are generally aware of the differences between fixed and random effects and whether they are performing analyses consistent with their consideration. All articles (excluding Notes and Comments) in Ecology and Evolution for the years 1990 and 1991 were reviewed. In general, authors that stated that their model contained both fixed and random effects correctly analyzed it as a mixed model. There were two cases, however, where authors attempted to define fixed effects as random in order to justify broader generalizations about the effects. Most commonly (63% of articles using two—way or greater ANOVA), authors neglected to mention whether they were dealing with a completely fixed, random, or mixed model. In such instances, it was not clear if the author was aware of the distinction between fixed and random effects, and it was often difficult to ascertain from the article whether their analysis was consistent with their experimental methods. These findings suggest several statistical guidelines that should be followed. In particular, the inclusion of explicit consideration of effects as fixed or random and clear descriptions of F tests of interest would provide the reader with confidence that the author has performed the analysis correctly. In addition, such an explicit statement would clarify the limits of the inferences about significant effects.

Maximum Likelihood Variance Components Estimation for Binary Data

Abstract: We consider a class of probit-normal models for binary data and describe ML and REML estimation of variance components for that class as well as best prediction for the realized values of the random effects. ML estimates are calculated using an EM algorithm; for complicated models EM includes a Gibbs step. The computations are illustrated through two examples.

Modeling Household Purchase Behavior with Logistic Normal Regression

Abstract: The successful development of marketing strategies requires the accurate measurement of household preferences and their reaction to variables such as price and advertising. Manufacturers, for examp...

Estimation of variance components for lamb weights in three sheep populations.

Abstract: Variance components were estimated for lamb weight at birth, 50 d, and 100 d of age. Data from the Canadian flock recording program for lambs born in 1977 to 1991 for Hampshires (n = 6,395) and Polled Dorsets (n = 29,204) and 1982 to 1991 for Romanovs (n = 3,432) were studied. Observed weights were pre-adjusted for the effects of age of dam, sex of lamb, birth-rearing type, month or quarter of year of birth, parity-lambing interval, and age of dam at first lambing, using estimates derived from a fixed effects model including contemporary groups plus these factors. Pre-adjusting for nuisance variables reduced the number of equations in the model for variance component estimation. A single-trait animal model with derivative-free restricted maximum-likelihood procedures was used. Random effects were additive direct and maternal genetic, litter (common environmental), and error. An alternate model excluded maternal genetic effects. Estimates of litter variance as a proportion of phenotypic variance were of moderate size (.12 to .43) and consistent across breeds and models. The mean correlation between direct and maternal genetic effects, across traits and breeds, weighted by the number of animals, was -.40 (SE = .15). The maternal genetic variance or direct-maternal genetic covariance component, or both, was different from zero (P < .05) for all traits in Hampshires and Polled Dorsets, suggesting that maternal effects were important for weight of lambs even at 100 d of age. Estimates of direct heritability ranged from .05 to .45, varying across traits, breeds, and models.(ABSTRACT TRUNCATED AT 250 WORDS)

Application of Random-Effects Probit Regression Models

Abstract: A random-effects probit model is developed for the case in which the outcome of interest is a series of correlated binary responses. These responses can be obtained as the product of a longitudinal response process where an individual is repeatedly classified on a binary outcome variable (e.g., sick or well on occasion t), or in "multilevel" or "clustered" problems in which individuals within groups (e.g., firms, classes, families, or clinics) are considered to share characteristics that produce similar responses. Both examples produce potentially correlated binary responses and modeling these person- or cluster-specific effects is required. The general model permits analysis at both the level of the individual and cluster and at the level at which experimental manipulations are applied (e.g., treatment group). The model provides maximum likelihood estimates for time-varying and time-invariant covariates in the longitudinal case and covariates which vary at the level of the individual and at the cluster level for multilevel problems. A similar number of individuals within clusters or number of measurement occasions within individuals is not required. Empirical Bayesian estimates of person-specific trends or cluster-specific effects are provided. Models are illustrated with data from mental health research.

Some approaches to the analysis of recurrent event data

Abstract: Methodological research in biostatistics has been dominated over the last twenty years by further development of Cox's regression model for life tables and of Nelder and Wedderburn's formulation of generalized linear models. In both of these areas the need to address the problems introduced by subject level heterogeneity has provided a major motivation, and the analysis of data concerning recurrent events has been widely discussed within both frameworks. This paper reviews this work, drawing together the parallel development of 'marginal' and 'conditional' approaches in survival analysis and in generalized linear models. Frailty models are shown to be a special case of a random effects generalization of generalized linear models, whereas marginal models for multivariate failure time data are more closely related to the generalized estimating equation approach to longitudinal generalized linear models. Computational methods for inference are discussed, including the Bayesian Markov chain Monte Carlo approach.

An introduction to the analysis of variance

Abstract: Preliminaries What We Do in an ANOVA Some Geometry of the ANOVA Two Factor Designs and Three Factor Designs Computations and Display Nested Factors Random Effects Models Repeated Measurement Designs Contrasting Effects Trend Tests Multiple Comparisons Regression, ANOVA, and the General Linear Model Some Fine Points Some Advanced Applications Nonorthogonal Designs Experimental Design Appendix 1: Random Variables and Their Expectations Appendix 2: Vectors and Matrices Appendix 3: Statistical Tables and Charts References Index

Influence of methodologic factors in a pooled analysis of 13 case-control studies of colorectal cancer and dietary fiber.

Abstract: We examined the study design features and data collection methods from 13 case-control studies of colorectal cancer and diet, which had been previously combined and analyzed, to determine whether they influenced the results obtained from a pooled analysis. We assessed the methods used in each study, estimated a quality score, and used random effects models to re-estimate the pooled odds ratio for the association between dietary fiber and colorectal cancer for these data. Key features of the methods used in each study and the quality score were examined in random effects models to determine whether the heterogeneity found between study-specific risk estimates could be explained by these variables. The odds ratio for dietary fiber and colorectal cancer was 0.46 (95% confidence interval = 0.34-0.64) for the 13 case-control studies as estimated with a random effects model. Two factors, whether the diet questionnaire had been validated before use in the case-control study and whether qualitative data on dietary habits and cooking methods had been incorporated into the nutrient estimation, explained some of the heterogeneity found between studies. Risk estimates for dietary fiber and colorectal cancer were closer to the null for the studies that had these two characteristics. Quality score did not explain any between-study heterogeneity. Random effects models, which included fixed effects covariates, explained some between-study heterogeneity in these data and would be useful for future pooled analyses.

A comparison of normal and nonnormal mixed models for number of lambs born in Norwegian sheep.

Abstract: A comparison of linear (LM), threshold (TM), and Poisson (PM) mixed models for genetic analysis of number of lambs born (NLB) from 1-yr-old ewes was conducted using 37,718 and 18,633 records of two Norwegian breeds, Dala and Spaelsau, respectively. Models fitted included flock-year as a fixed effect and the random effect of sire. In the Poisson model, the residual variation was assumed to be Poisson, whereas it was normal in LM and multinomial in TM. The models were compared with respect to goodness of fit, predictive ability, and ranking of sires. Goodness of fit and predictive ability were assessed via the mean squared error and the correlation between observed NLB and fitted (predicted) values. Predictive ability was evaluated by estimating effects of sire and flock-year using a random half of the data and then using these estimates to predict records on the other half of the data. The heritability of NLB for Dala was estimated to be .20, .39, and .08 with LM, TM, and PM, respectively. For Spaelsau, corresponding estimates were .12, .26, and .00, respectively. In the PM, problems of low or zero estimates of sire variances were encountered. Hence, an alternative sire variance (PM-L) was approximated from the heritability estimated on the outward scale by REML. All models performed similarly with respect to goodness of fit, predictive ability, and ranking of sires. The TM was very slightly better for both breeds, but the PM and PM-L seemed clearly poorer than TM and LM. An approximate test rejected the hypothesis that the conditional distribution of NLB was Poisson.

Some Applications of Radial Plots

Abstract: A radial plot is a graphical display for comparing estimates that have differing precisions. It is a scatter plot of standardized estimates against reciprocals of standard errors, possibly with respect to a transformed scale, designed so that the original estimates can be compared and interpreted. The estimates may be means, regression coefficients, proportions, rates, odds ratios, random effects, or indeed any parameter estimates that merit comparison between individuals or groups. This article illustrates some uses of radial plots by discussing a variety of data examples taken from the literature. The statistical application areas include interlaboratory trials, point process event rates, empirical Bayes estimation, modeling of counting data, analysis of overdispersed and underdispersed binomial and Poisson data, mixture modeling and meta-analysis.

A One-Way Random Effects Model for Trimmed Means.

Abstract: The random effects ANOVA model plays an important role in many psychological studies, but the usual model suffers from at least two serious problems. The first is that even under normality, violating the assumption of equal variances can have serious consequences in terms of Type I errors or significance levels, and it can affect power as well. The second and perhaps more serious concern is that even slight departures from normality can result in a substantial loss of power when testing hypotheses. Jeyaratnam and Othman (1985) proposed a method for handling unequal variances, under the assumption of normality, but no results were given on how their procedure performs when distributions are nonnormal. A secondary goal in this paper is to address this issue via simulations. As will be seen, problems arise with both Type I errors and power. Another secondary goal is to provide new simulation results on the Rust-Fligner modification of the Kruskal-Wallis test. The primary goal is to propose a generalization of the usual random effects model based on trimmed means. The resulting test of no differences among J randomly sampled groups has certain advantages in terms of Type I errors, and it can yield substantial gains in power when distributions have heavy tails and outliers. This last feature is very important in applied work because recent investigations indicate that heavy-tailed distributions are common. Included is a suggestion for a heteroscedastic Winsorized analog of the usual intraclass correlation coefficient.

Adaptive Estimation in the Panel Data Error Component Model with Heteroskedasticity of Unknown Form

Abstract: The authors show that the adaptive estimation result for the heteroskedasticity of an unknown form time-series (or cross-section) model can be generalized to the panel data error components model. The authors give recursive transformations that change the error term of a random effects model and the first differenced error term of a fixed effects model into classical errors. They also propose a modified Breusch-Pagan test for testing the random individual effects. Monte Carlo evidence suggests that the proposed estimator performs adequately in small samples. Copyright 1994 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

The Gender Gap in Earnings: A Two-Way Nested Multiple Regression Analysis with Random Effects

Abstract: The gender income gap is a much debated subject both at an analytical and economic level. This article considers both, but emphasizes the different ways the data can be analyzed. The authors show that a hierarchical linear model is the best way to evaluate male-female wage differentials. Both interindustry and intraindustry wage disparities between men and women are measured by using a technique that assumes that observations within the same industry have correlated error terms. By simultaneously testing human capital factors and environmental factors, the analysis model serves as a link between theory and empirical analysis. The results show that the wage differences are larger in some industries than in others, so that it can be assumed that a gender income gap is not only a function of individual differences in qualification, but also differences between industries. The between-industry differences in gender income gaps contradict the hypothesis that gender income differential is largely due to female ...

Multivariate survival analysis using piecewise gamma frailty.

Abstract: In this note we propose a frailty model called piecewise gamma frailty for correlated survival data with random effects having a nested structure. In frailty models, a dependence function defined as a hazard ratio of one member given the failure time of another member in a unit is determined by the distributional assumptions on frailty. In the piecewise gamma frailty model, the nested structure of random effects or frailty allows the dependence function to vary over the time periods. This model includes existing models such as the piecewise exponential model (Breslow, 1974, Biometrics 30, 89-100) and the gamma frailty model (Clayton, 1978, Biometrika 65, 141-151; Oakes, 1982, Journal of the Royal Statistical Society, Series B 44, 414-428) as special cases. A study of familial aggregation of epilepsy is used to illustrate the proposed method.

Interpretation of sugar maple (Acersaccharum) ring chronologies from central and southern Ontario using a mixed linear model

Abstract: This study presents a new method for assessing the impact of environmental factors on the radial growth rate of trees. The natural logarithm of the specific volume increments (SVI) were fitted to a mixed linear model, which included fixed effects for tree age when the increment occurs, year, precipitation, and temperature both in the year of growth and in the preceding year, and the geographical locale. The model also incorporates stand and tree as random effects. By fitting trees of different ages, the model is able to separate year effects from age effects. Age and year were treated as categorical variables and hence no specific form of growth curve is assumed. The model was fitted to log SVI from 84 mature sugar maple (Acersaccharum Marsh.) trees from 42 uneven-aged stands in six regions of southern and central Ontario representing a known gradient of air pollution. After adjusting for age, precipitation, and temperature effects, the log SVI increased during the first half and declined during the secon...

Analysis of clustered data in community psychology: with an example from a worksite smoking cessation project.

Abstract: Although it is common in community psychology research to have data at both the community, or cluster, and individual level, the analysis of such clustered data often presents difficulties for many researchers. Since the individuals within the cluster cannot be assumed to be independent, the use of many traditional statistical techniques that assumes independence of observations is problematic. Further, there is often interest in assessing the degree of dependence in the data resulting from the clustering of individuals within communities. In this paper, a random-effects regression model is described for analysis of clustered data. Unlike ordinary regression analysis of clustered data, random-effects regression models do not assume that each observation is independent, but do assume data within clusters are dependent to some degree. The degree of this dependency is estimated along with estimates of the usual model parameters, thus adjusting these effects for the dependency resulting from the clustering of the data. Models are described for both continuous and dichotomous outcome variables, and available statistical software for these models is discussed. An analysis of a data set where individuals are clustered within firms is used to illustrate fetatures of random-effects regression analysis, relative to both individual-level analysis which ignores the clustering of the data, and cluster-level analysis which aggregates the individual data.

Testing for omitted variables and non-linearity in regression models for longitudinal data

Abstract: When fitting regression models to investigate the relationship between an outcome variable and independent variables of primary interest, there is often concern whether omitted variables or assuming a different functional relationship could have changed the conclusion or interpretation of the results. In longitudinal studies of aging, the concern with omitted variables is well known in the context of cohort and period effects, which refer to unmeasured variables systematically related to the individual's year of birth and secular trends in outcome, respectively. We present and compare three approaches to detecting omitted confounders and non-linearity in the random effects model for longitudinal data (Laird and Ware, 1982) with random slope and intercept across individuals. The first approach compares simple unweighted within and between regression coefficients, the second is the Hausman specification test for regression models, and the third approach involves testing directly the significance of functions of individual specific covariate means means i, in the random effects regression model. This last approach is motivated by the models that arise when cohort or period effects are ignored. We compare the three approaches, and illustrate their application.

Test of homogeneity of binary data with explanatory variables.

Abstract: SUMMARY Apparent heterogeneity of the risk of a disease in different groups may be explained by subjectspecific risk factors unequally distributed in these groups. We propose a score test of homogeneity that allows adjustment for known risk factors of the disease. The test is based oni a random-effect logistic regression model and requires only simple computations in addition to a conventional logistic regression method. The score test is applied to the study of geographical heterogeneity of cognitive impairment in elderly using a sample of 3,318 subjects scattered in 75 parishes. It is shown that an apparent heterogeneity disappears when taking into account subject-specific risk factors. This test may also be useful for studying familial aggregation of a disease. Testing homogeneity of the distribution of binary traits in different groups has long been recognized as an important problem, particularly in conventional genetics (Smith, 1951) and in genetic epidemiology, where it may be used to investigate the familial aggregation of a disease. The presence of familial aggregation suggests a genetic determinant. Testing homogeneity of geographical units is also of interest: the presence of heterogeneity suggests the presence of an unmeasured environmental factor. Another application occurs if the possible correlation of the data is treated as a nuisance: it is useful to test whether the groups are homogeneous before performing ordinary regression models (Liang, 1987). Chi-squared tests are used for testing homogeneity when the number of groups is small. However the chi-squared test is not applicable when the sizes of the groups are not large (Haldane, 1940) and when the number of groups is large. In such cases random-effect models are preferred: the probability of disease within a group have a common distribution. Thus the null hypothesis is specified by a null variance of the random effect and alternative hypotheses are specified by a unique parameter, the variance of the random effect, whatever the number of groups (see Potthoff and Whittinghill, 1966; Wisniewsky, 1968; and Tarone, 1979). In epidemiologic studies, however, we often need to test for homogeneity while adjusting for other risk factors of the disease. Indeed, risk factors, if differently distributed in the different groups, may play the role of confounding factors relative to the group effect. It is of paramount importance in genetic studies to investigate whether an apparent familial aggregation may be explained by nongenetic factors such as educational level or nutritional habits which may also segregate in families. Similarly, geographical clusters may be explained by nonenvironmental factors unequally distributed in the geographical units. Based on a random-effect logistic regression model, we derive a score test of homogeneity that allows adjustment on explanatory variables. The score statistic is the same as that proposed by Hamerle (1990) in the context of repeated measurements but the variance proposed in the present paper is different. Simulations show that it leads to a more powerful test. We use this test to investigate the possible geographical heterogeneity of cognitive impairment as measured by the Mini-Mental State score in 3,318 subjects scattered in 75 parishes in southwestern France.

Random-effects linear regression meta-analysis models with application to the nitrogen dioxide health effects studies.

Abstract: As the field of epidemiology grows and multiple studies of the same topic are more frequently available, increased focus is placed on quantitative methods for synthesis of results to yield an overa...

Subject-specific and Population-averaged Continuation Ratio Logit Models for Multiple Discrete Time Survival Profiles

Abstract: SUMMARY Subject-specific and population-averaged continuation ratio logit models are presented for multivariate discrete time survival data. The models characterize data from a psychological experiment by using a quadratic polynomial relationship across time that depends on a time-independent condition. A multivariate normal random effects distribution is imposed on intercept, linear and quadratic terms in the subject-specific model, which is fitted by using a combination of Gibbs sampling and buffered stochastic substitution. Variance components that tend towards 0 are addressed in this context. In addition, generalized estimating equations estimates of the parameters in the population-averaged model are compared with analogous estimates for the mixed effects model.